def make_obs_br(M, l): """Make observable instances for branching ratios""" _process_tex = _hadr[M]['tex'] + _tex[l] + r"^+" + _tex[l] + r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$" B = _hadr[M]['B'] V = _hadr[M]['V'] # binned branching ratio _obs_name = "<dBR/dq2>(" + M + l + l + ")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Binned differential branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\langle \frac{d\text{BR}}{dq^2} \rangle(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) func = lambda wc_obj, par, q2min, q2max: BVll_dBRdq2_int( q2min, q2max, B, V, l, wc_obj, par)() Prediction(_obs_name, func) # differential branching ratio _obs_name = "dBR/dq2(" + M + l + l + ")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(r"Differential branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) func = lambda wc_obj, par, q2: BVll_dBRdq2(q2, B, V, l, wc_obj, par)() Prediction(_obs_name, func)
def _define_obs_B_Mll(M, ll): _process_tex = _hadr_lfv[M]['tex']+' '+_tex_lfv[''.join(ll)] _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to P\ell^+\ell^-$ :: $' + _process_tex + r"$" _obs_name = "BR("+M+''.join(ll)+")" _obs = Observable(_obs_name) _obs.set_description(r"Total branching ratio of $"+_process_tex+r"$") _obs.tex = r"$\text{BR}(" + _process_tex+r")$" _obs.add_taxonomy(_process_taxonomy) return _obs_name
def make_metadata_binned(M, l, obs, obsdict): _process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$" B = _hadr[M]['B'] V = _hadr[M]['V'] _obs_name = "<" + obs + ">("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description('Binned ' + obsdict['desc'] + r" in $" + _process_tex + r"$") _obs.tex = r"$\langle " + obsdict['tex'] + r"\rangle(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) return _obs
def make_metadata_differential(M, l, obs, obsdict): _process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$" B = _hadr[M]['B'] V = _hadr[M]['V'] _obs_name = obs + "("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(obsdict['desc'][0].capitalize() + obsdict['desc'][1:] + r" in $" + _process_tex + r"$") _obs.tex = r"$" + obsdict['tex'] + r"(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) return _obs
def make_metadata_binned(M, l, obs, obsdict): _process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$" B = _hadr[M]['B'] V = _hadr[M]['V'] _obs_name = "<" + obs + ">("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description('Binned ' + obsdict['desc'] + r" in $" + _process_tex + r"$") _obs.tex = r"$\langle " + obsdict['tex'] + r"\rangle(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) return _obs
def make_metadata_differential(M, l, obs, obsdict): _process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$" B = _hadr[M]['B'] V = _hadr[M]['V'] _obs_name = obs + "("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(obsdict['desc'][0].capitalize() + obsdict['desc'][1:] + r" in $" + _process_tex + r"$") _obs.tex = r"$" + obsdict['tex'] + r"(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) return _obs
def make_obs_neutron_corr(coeff, me_E=False): _process_tex = r"n\to p^+ e^-\bar\nu_e" _process_taxonomy = r'Process :: Nucleon decays :: Beta decays :: Neutron decay :: $' + _process_tex + r"$" _obs_name = coeff + "_n" if me_E: _obs = Observable(_obs_name, arguments=['me_E']) else: _obs = Observable(_obs_name) _obs.set_description(r"Correlation coefficient $" + tex + r"$ in neutron beta decay") _obs.tex = r"$" + tex + r"$" _obs.add_taxonomy(_process_taxonomy) if me_E: func = lambda wc_obj, par, me_E: Neutron_corr(wc_obj, par, me_E, coeff)() else: func = lambda wc_obj, par: Neutron_corr(wc_obj, par, None, coeff)() Prediction(_obs_name, func)
def make_obs_lfur(M, l): """Make observable instances for lepton flavour ratios""" # binned ratio of BRs _obs_name = "<R" + l[0] + l[1] + ">(" + M + "ll)" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Ratio of partial branching ratios of $" + _hadr[M]['tex'] + _tex[l[0]] + r"^+ " + _tex[l[0]] + r"^-$" + " and " + r"$" + _hadr[M]['tex'] + _tex[l[1]] + r"^+ " + _tex[l[1]] + "^-$") _obs.tex = r"$\langle R_{" + _tex[l[0]] + ' ' + _tex[ l[1]] + r"} \rangle(" + _hadr[M]['tex'] + r"\ell^+\ell^-)$" for li in l: # add taxonomy for both processes (e.g. B->Vee and B->Vmumu) _obs.add_taxonomy( r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _hadr[M]['tex'] + _tex[li] + r"^+" + _tex[li] + r"^-$") Prediction( _obs_name, bvll_obs_int_ratio_leptonflavour(dGdq2_ave, _hadr[M]['B'], _hadr[M]['V'], *l)) # differential ratio of BRs _obs_name = "R" + l[0] + l[1] + "(" + M + "ll)" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(r"Ratio of differential branching ratios of $" + _hadr[M]['tex'] + _tex[l[0]] + r"^+ " + _tex[l[0]] + r"^-$" + " and " + r"$" + _hadr[M]['tex'] + _tex[l[1]] + r"^+ " + _tex[l[1]] + "^-$") _obs.tex = r"$R_{" + _tex[l[0]] + ' ' + _tex[ l[1]] + r"} (" + _hadr[M]['tex'] + r"\ell^+\ell^-)$" for li in l: # add taxonomy for both processes (e.g. B->Vee and B->Vmumu) _obs.add_taxonomy( r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _hadr[M]['tex'] + _tex[li] + r"^+" + _tex[li] + r"^-$") func = lambda wc_obj, par, q2: BVll_dBRdq2(q2, B, V, l, wc_obj, par)() Prediction( _obs_name, bvll_obs_ratio_leptonflavour(dGdq2_ave, _hadr[M]['B'], _hadr[M]['V'], *l))
def make_obs_lfur(M, l): """Make observable instances for lepton flavour ratios""" # binned ratio of BRs _obs_name = "<R"+l[0]+l[1]+">("+M+"ll)" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Ratio of partial branching ratios of $" + _hadr[M]['tex'] +_tex[l[0]]+r"^+ "+_tex[l[0]]+r"^-$" + " and " + r"$" + _hadr[M]['tex'] +_tex[l[1]]+r"^+ "+_tex[l[1]]+"^-$") _obs.tex = r"$\langle R_{" + _tex[l[0]] + ' ' + _tex[l[1]] + r"} \rangle(" + _hadr[M]['tex'] + r"\ell^+\ell^-)$" for li in l: # add taxonomy for both processes (e.g. B->Vee and B->Vmumu) _obs.add_taxonomy(r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _hadr[M]['tex'] +_tex[li]+r"^+"+_tex[li]+r"^-$") Prediction(_obs_name, bvll_obs_int_ratio_leptonflavour(dGdq2_ave, _hadr[M]['B'], _hadr[M]['V'], *l)) # differential ratio of BRs _obs_name = "R"+l[0]+l[1]+"("+M+"ll)" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(r"Ratio of differential branching ratios of $" + _hadr[M]['tex'] +_tex[l[0]]+r"^+ "+_tex[l[0]]+r"^-$" + " and " + r"$" + _hadr[M]['tex'] +_tex[l[1]]+r"^+ "+_tex[l[1]]+"^-$") _obs.tex = r"$R_{" + _tex[l[0]] + ' ' + _tex[l[1]] + r"} (" + _hadr[M]['tex'] + r"\ell^+\ell^-)$" for li in l: # add taxonomy for both processes (e.g. B->Vee and B->Vmumu) _obs.add_taxonomy(r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _hadr[M]['tex'] +_tex[li]+r"^+"+_tex[li]+r"^-$") func = lambda wc_obj, par, q2: BVll_dBRdq2(q2, B, V, l, wc_obj, par)() Prediction(_obs_name, bvll_obs_ratio_leptonflavour(dGdq2_ave, _hadr[M]['B'], _hadr[M]['V'], *l))
def make_obs_br(M, l): """Make observable instances for branching ratios""" _process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$" B = _hadr[M]['B'] V = _hadr[M]['V'] # binned branching ratio _obs_name = "<dBR/dq2>("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Binned differential branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\langle \frac{d\text{BR}}{dq^2} \rangle(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) func = lambda wc_obj, par, q2min, q2max: BVll_dBRdq2_int(q2min, q2max, B, V, l, wc_obj, par)() Prediction(_obs_name, func) # differential branching ratio _obs_name = "dBR/dq2("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(r"Differential branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) func = lambda wc_obj, par, q2: BVll_dBRdq2(q2, B, V, l, wc_obj, par)() Prediction(_obs_name, func)
wc_s = flavio.physics.bdecays.wilsoncoefficients.wctot_dict(wc_obj, "bsee", scale, par, nf_out=5) br_d = abs(xi_t_d) ** 2 * PE0_BR_BXgamma(wc_d, par, "d", E0) br_s = abs(xi_t_s) ** 2 * PE0_BR_BXgamma(wc_s, par, "s", E0) as_d = abs(xi_t_d) ** 2 * PE0_ACP_BXgamma(wc_d, par, "d", E0) as_s = abs(xi_t_s) ** 2 * PE0_ACP_BXgamma(wc_s, par, "s", E0) # return (as_s)/(br_s + br_d) return (as_s + as_d) / (br_s + br_d) _process_taxonomy = r"Process :: $b$ hadron decays :: FCNC decays :: $B\to X\gamma$ :: " _obs_name = "BR(B->Xsgamma)" _obs = Observable(_obs_name) _obs.set_description(r"CP-averaged branching ratio of $B\to X_s\gamma$ for $E_\gamma>1.6$ GeV") _obs.tex = r"$\text{BR}(B\to X_s\gamma)$" _obs.add_taxonomy(_process_taxonomy + r"$B\to X_s\gamma$") Prediction(_obs_name, lambda wc_obj, par: BRBXgamma(wc_obj, par, "s", 1.6)) _obs_name = "BR(B->Xdgamma)" _obs = Observable(_obs_name) _obs.set_description(r"CP-averaged branching ratio of $B\to X_d\gamma$ for $E_\gamma>1.6$ GeV") _obs.tex = r"$\text{BR}(B\to X_d\gamma)$" _obs.add_taxonomy(_process_taxonomy + r"$B\to X_d\gamma$") Prediction(_obs_name, lambda wc_obj, par: BRBXgamma(wc_obj, par, "d", 1.6)) _obs_name = "ACP(B->Xgamma)" _obs = Observable(_obs_name) _obs.set_description(r"Direct CP asymmetry in $B\to X_{s+d}\gamma$ for $E_\gamma>1.6$ GeV") _obs.tex = r"$A_\text{CP}(B\to X_{s+d}\gamma)$" _obs.add_taxonomy(_process_taxonomy + r"$B\to X_{s+d}\gamma$") Prediction(_obs_name, lambda wc_obj, par: ACPBXgamma(wc_obj, par, 1.6))
br_d = abs(xi_t_d)**2 * PE0_BR_BXgamma(wc_d, par, 'd', E0) br_s = abs(xi_t_s)**2 * PE0_BR_BXgamma(wc_s, par, 's', E0) as_d = abs(xi_t_d)**2 * PE0_ACP_BXgamma(wc_d, par, 'd', E0) as_s = abs(xi_t_s)**2 * PE0_ACP_BXgamma(wc_s, par, 's', E0) # return (as_s)/(br_s + br_d) return (as_s + as_d) / (br_s + br_d) _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to X\gamma$ :: ' _obs_name = "BR(B->Xsgamma)" _obs = Observable(_obs_name) _obs.set_description( r"CP-averaged branching ratio of $B\to X_s\gamma$ for $E_\gamma>1.6$ GeV") _obs.tex = r"$\text{BR}(B\to X_s\gamma)$" _obs.add_taxonomy(_process_taxonomy + r"$B\to X_s\gamma$") Prediction(_obs_name, lambda wc_obj, par: BRBXgamma(wc_obj, par, 's', 1.6)) _obs_name = "BR(B->Xdgamma)" _obs = Observable(_obs_name) _obs.set_description( r"CP-averaged branching ratio of $B\to X_d\gamma$ for $E_\gamma>1.6$ GeV") _obs.tex = r"$\text{BR}(B\to X_d\gamma)$" _obs.add_taxonomy(_process_taxonomy + r"$B\to X_d\gamma$") Prediction(_obs_name, lambda wc_obj, par: BRBXgamma(wc_obj, par, 'd', 1.6)) _obs_name = "ACP(B->Xgamma)" _obs = Observable(_obs_name) _obs.set_description( r"Direct CP asymmetry in $B\to X_{s+d}\gamma$ for $E_\gamma>1.6$ GeV") _obs.tex = r"$A_\text{CP}(B\to X_{s+d}\gamma)$"
return (-par['omega+'] / (sqrt(2) * par['eps_K']) * (ImA0 / ReA0 * (1 - par['Omegahat_eff']) - 1 / a * ImA2 / ReA2).real) def epsprime_NP(wc_obj, par): r"""Compute the NP contribution to $\epsilon'/\epsilon$.""" # Neglecting isospin breaking corrections! A = Kpipi_amplitudes_NP(wc_obj, par) ImA0 = A[0].imag ImA2 = A[2].imag ReA0 = par['ReA0(K->pipi)'] ReA2 = par['ReA2(K->pipi)'] a = par['epsp a'] # eq. (16) # dividing by a to remove the isospin brk corr in omega+, cf. (16) in 1507.06345 return (-par['omega+'] / a / (sqrt(2) * par['eps_K']) * (ImA0 / ReA0 - ImA2 / ReA2).real) def epsprime(wc_obj, par): r"""Compute $\epsilon'/\epsilon$, parametrizing direct CPV in $K\to\pi\pi$.""" return epsprime_SM(par) + epsprime_NP(wc_obj, par) # Observable and Prediction instances o = Observable('epsp/eps') o.tex = r"$\epsilon^\prime/\epsilon$" Prediction('epsp/eps', epsprime) o.set_description(r"Direct CP violation parameter") o.add_taxonomy(r'Process :: $s$ hadron decays :: Non-leptonic decays :: $K\to \pi\pi$')
'Bs->phi': {'tex': r"B_s\to \phi ", 'B': 'Bs', 'V': 'phi', }, } for l in ['e', 'mu', 'tau']: for M in _hadr.keys(): _process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$" for obs in sorted(_observables.keys()): # binned angular observables _obs_name = "<" + obs + ">("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description('Binned ' + _observables[obs]['desc'] + r" in $" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-$") _obs.tex = r"$\langle " + _observables[obs]['tex'] + r"\rangle(" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-)$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, bsvll_obs_int_ratio_func(_observables[obs]['func_num'], SA_den_Bs, _hadr[M]['B'], _hadr[M]['V'], l)) # differential angular observables _obs_name = obs + "("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(_observables[obs]['desc'][0].capitalize() + _observables[obs]['desc'][1:] + r" in $" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-$") _obs.tex = r"$" + _observables[obs]['tex'] + r"(" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-)$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, bsvll_obs_ratio_func(_observables[obs]['func_num'], SA_den_Bs, _hadr[M]['B'], _hadr[M]['V'], l)) # binned branching ratio _obs_name = "<dBR/dq2>("+M+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Binned time-integrated differential branching ratio of $" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-$") _obs.tex = r"$\langle \frac{d\overline{\text{BR}}}{dq^2} \rangle(" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-)$"
def BR_tot_leptonflavour_function(lnum, lden): return lambda wc_obj, par: BR_tot_leptonflavour(wc_obj, par, lnum, lden) _process_taxonomy = r'Process :: $b$ hadron decays :: Semi-leptonic tree-level decays :: $B\to X\ell\nu$ :: $' _lep = {'e': 'e', 'mu': r'\mu', 'tau': r'\tau', 'l': r'\ell'} for l in _lep: _obs_name = "BR(B->Xc" + l + "nu)" _process_tex = r"B\to X_c" + _lep[l] + r"^+\nu_" + _lep[l] _obs = Observable(_obs_name) _obs.set_description(r"Total branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\text{BR}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy + _process_tex + r"$") Prediction(_obs_name, BR_tot_function(l)) # Lepton flavour ratios for l in [('mu', 'e'), ('tau', 'mu'), ('tau', 'l')]: _obs_name = "R" + l[0] + l[1] + "(B->Xclnu)" _obs = Observable(name=_obs_name) _process_1 = r"B\to X_c" + _lep[l[0]] + r"^+\nu_" + _lep[l[0]] _process_2 = r"B\to X_c" + _lep[l[1]] + r"^+\nu_" + _lep[l[1]] _obs.set_description(r"Ratio of total branching ratios of $" + _process_1 + r"$" + " and " + r"$" + _process_2 + r"$") _obs.tex = r"$R_{" + _lep[l[0]] + ' ' + _lep[ l[1]] + r"}(B\to X_c\ell^+\nu)$" # add taxonomy for both processes (e.g. B->Xcenu and B->Xcmunu) _obs.add_taxonomy(_process_taxonomy + _process_1 + r"$") _obs.add_taxonomy(_process_taxonomy + _process_2 + r"$")
(1 - par['Omegahat_eff']) - 1 / a * ImA2 / ReA2).real) def epsprime_NP(wc_obj, par): r"""Compute the NP contribution to $\epsilon'/\epsilon$.""" # Neglecting isospin breaking corrections! A = Kpipi_amplitudes_NP(wc_obj, par) ImA0 = A[0].imag ImA2 = A[2].imag ReA0 = par['ReA0(K->pipi)'] ReA2 = par['ReA2(K->pipi)'] a = par['epsp a'] # eq. (16) # dividing by a to remove the isospin brk corr in omega+, cf. (16) in 1507.06345 return (-par['omega+'] / a / (sqrt(2) * par['eps_K']) * (ImA0 / ReA0 - ImA2 / ReA2).real) def epsprime(wc_obj, par): r"""Compute $\epsilon'/\epsilon$, parametrizing direct CPV in $K\to\pi\pi$.""" return epsprime_SM(par) + epsprime_NP(wc_obj, par) # Observable and Prediction instances o = Observable('epsp/eps') o.tex = r"$\epsilon^\prime/\epsilon$" Prediction('epsp/eps', epsprime) o.set_description(r"Direct CP violation parameter") o.add_taxonomy( r'Process :: $s$ hadron decays :: Non-leptonic decays :: $K\to \pi\pi$')
# Observable and Prediction instances _tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau'} for l in ['e', 'mu', 'tau']: _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to\ell^+\ell^-$ :: $' # For the Bs decay, we take the time-integrated branching ratio _obs_name = "BR(Bs->" + l + l + ")" _obs = Observable(_obs_name) _process_tex = r"B_s\to " + _tex[l] + r"^+" + _tex[l] + r"^-" _obs.set_description(r"Time-integrated branching ratio of $" + _process_tex + r"$.") _obs.tex = r"$\overline{\text{BR}}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy + _process_tex + r"$") Prediction(_obs_name, bqll_obs_function(br_timeint, 'Bs', l, l)) # Add the effective lifetimes for Bs _obs_name = 'tau_' + l + l _obs = Observable(_obs_name) _obs.set_description(r"Effective lifetime for $" + _process_tex + r"$.") _obs.tex = r"$\tau_{B_s \to " + _tex[l] + _tex[l] + "}$" _obs.add_taxonomy(_process_taxonomy + _process_tex + r"$") if l == 'e': Prediction(_obs_name, lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'e')) if l == 'mu': Prediction(_obs_name, lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'mu')) if l == 'tau':
def CR_mueAl(wc_obj, par): r"""Conversion rate for $\phantom k^{27}_{13} \mathrm{Al}$""" return CR_mue(wc_obj, par, 'Al') def CR_mueTi(wc_obj, par): r"""Conversion rate for $\phantom k^{48}_{22} \mathrm{Ti}$""" return CR_mue(wc_obj, par, 'Ti') CRAu = Observable('CR(mu->e, Au)') Prediction('CR(mu->e, Au)', CR_mueAu) CRAu.tex = r"$CR(\mu - e)$ in $\phantom k^{197}_{79} \mathrm{Au}$" CRAu.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{197}_{79} \mathrm{Au}$" CRAu.add_taxonomy( r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRAu.tex) CRAl = Observable('CR(mu->e, Al)') Prediction('CR(mu->e, Al)', CR_mueAl) CRAl.tex = r"$CR(\mu - e)$ in $\phantom k^{27}_{13} \mathrm{Al}$" CRAl.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{27}_{13} \mathrm{Al}$" CRAl.add_taxonomy( r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRAl.tex) CRTi = Observable('CR(mu->e, Ti)') Prediction('CR(mu->e, Ti)', CR_mueTi) CRTi.tex = r"$CR(\mu - e)$ in $\phantom k^{48}_{22} \mathrm{Ti}$" CRTi.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{48}_{22} \mathrm{Ti}$" CRTi.add_taxonomy( r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRTi.tex)
'FL': {'func_num': FL_num, 'tex': r'F_L', 'desc': 'longitudinal polarization fraction'}, 'AFBl': {'func_num': AFBl_num, 'tex': r'A_\text{FB}^\ell', 'desc': 'leptonic forward-backward asymmetry'}, 'AFBh': {'func_num': AFBh_num, 'tex': r'A_\text{FB}^h', 'desc': 'hadronic forward-backward asymmetry'}, 'AFBlh': {'func_num': AFBlh_num, 'tex': r'A_\text{FB}^{\ell h}', 'desc': 'lepton-hadron forward-backward asymmetry'}, } for l in ['e', 'mu', ]: # tau requires lepton mass dependence! _process_tex = r"\Lambda_b\to\Lambda " +_tex[l]+r"^+"+_tex[l]+r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $\Lambda_b\to \Lambda\ell^+\ell^-$ :: $' + _process_tex + r"$" # binned branching ratio _obs_name = "<dBR/dq2>(Lambdab->Lambda"+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Binned differential branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\langle \frac{d\text{BR}}{dq^2} \rangle(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, dbrdq2_int_func(l)) # differential branching ratio _obs_name = "dBR/dq2(Lambdab->Lambda"+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(r"Differential branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, dbrdq2_func(l)) for obs in _observables: # binned angular observables _obs_name = "<" + obs + ">(Lambdab->Lambda"+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description("Binned " + _observables[obs]['desc'] + r" in $" + _process_tex + r"$")
# Observable instances _tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau', 'l': r'\ell'} for l in ['e', 'mu', 'tau', 'l']: for q in ['s', 'd']: _process_tex = r"B\to X_" + q +_tex[l]+r"^+"+_tex[l]+r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to X\ell^+\ell^-$ :: $' + _process_tex + r"$" # binned branching ratio _obs_name = "<BR>(B->X"+q+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Binned branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\langle \text{BR} \rangle(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, bxll_br_int_func(q, l)) # differential branching ratio _obs_name = "dBR/dq2(B->X"+q+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(r"Differential branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, bxll_dbrdq2_func(q, l)) if l != 'tau': # AFB not yet implemented for tau! (ml=0) # binned AFB _obs_name = "<AFB>(B->X"+q+l+l+")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
for l in ['e', 'mu', 'tau', 'l']: for br in ['dBR/dq2', 'BR', '<BR>', 'dBR_L/dq2', 'BR_L', '<BR_L>', 'dBR_T/dq2', 'BR_T', '<BR_T>', '<BR>/<cl>', '<BR>/<cV>', '<BR>/<phi>', 'dBR/dcl', 'dBR/dcV', 'dBR/dphi', '<FL>', 'FL', 'FLtot']: for M in _hadr.keys(): _process_tex = _hadr[M]['tex']+_tex[l]+r"^+\nu_"+_tex[l] _obs_name = br + "("+M+l+"nu)" _obs = Observable(_obs_name) _obs.set_description(_desc[br] + r" branching ratio of $" + _process_tex + "$") _obs.tex = r'$' + _tex_br[br] + r"(" +_process_tex + ")$" _obs.arguments = _args[br] _obs.add_taxonomy(_process_taxonomy + _process_tex + r'$') if br in _A: # for dBR/dq2, need to distinguish between total, L, and T Prediction(_obs_name, _func[br](_hadr[M]['B'], _hadr[M]['V'], l, A=_A[br])) else: # for other observables not Prediction(_obs_name, _func[br](_hadr[M]['B'], _hadr[M]['V'], l)) # Lepton flavour ratios for l in [('mu','e'), ('tau','mu'), ('tau', 'l')]: for M in _hadr_l.keys(): # binned ratio of BRs _obs_name = "<R"+l[0]+l[1]+">("+M+"lnu)" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
xi = etaCP * qp * A / A_bar return -2*xi.imag / ( 1 + abs(xi)**2 ) def S_BJpsiK(wc_obj, par): return S(wc_obj, par, 'B0', amplitude_BJpsiK, etaCP=-1) def S_Bspsiphi(wc_obj, par): return S(wc_obj, par, 'Bs', amplitude_Bspsiphi, etaCP=+1) # Observable and Prediction instances o = Observable('DeltaM_s') o.set_description(r"Mass difference in the $B_s$-$\bar B_s$ system") o.tex = r"$\Delta M_s$" o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B_s$-$\bar B_s$ mixing') Prediction('DeltaM_s', lambda wc_obj, par: DeltaM(wc_obj, par, 'Bs')) o = Observable('DeltaM_d') o.set_description(r"Mass difference in the $B^0$-$\bar B^0$ system") o.tex = r"$\Delta M_d$" o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B^0$-$\bar B^0$ mixing') Prediction('DeltaM_d', lambda wc_obj, par: DeltaM(wc_obj, par, 'B0')) o = Observable('a_fs_s') o.set_description(r"CP asymmetry in flavour-specific $B_s$ decays") o.tex = r"$a_\text{fs}^s$" o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B_s$-$\bar B_s$ mixing') Prediction('a_fs_s', lambda wc_obj, par: a_fs(wc_obj, par, 'Bs')) o = Observable('a_fs_d')
# Observable instances _tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau', 'l': r'\ell'} for l in ['e', 'mu', 'tau', 'l']: for q in ['s', 'd']: _process_tex = r"B\to X_" + q + _tex[l] + r"^+" + _tex[l] + r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to X\ell^+\ell^-$ :: $' + _process_tex + r"$" # binned branching ratio _obs_name = "<BR>(B->X" + q + l + l + ")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Binned branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\langle \text{BR} \rangle(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, bxll_br_int_func(q, l)) # differential branching ratio _obs_name = "dBR/dq2(B->X" + q + l + l + ")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(r"Differential branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, bxll_dbrdq2_func(q, l)) if l != 'tau': # AFB not yet implemented for tau! (ml=0) # binned AFB _obs_name = "<AFB>(B->X" + q + l + l + ")"
xi = etaCP * qp * A / A_bar return -2*xi.imag / ( 1 + abs(xi)**2 ) def S_BJpsiK(wc_obj, par): return S(wc_obj, par, 'B0', amplitude_BJpsiK, etaCP=-1) def S_Bspsiphi(wc_obj, par): return S(wc_obj, par, 'Bs', amplitude_Bspsiphi, etaCP=+1) # Observable and Prediction instances o = Observable('DeltaM_s') o.set_description(r"Mass difference in the $B_s$-$\bar B_s$ system") o.tex = r"$\Delta M_s$" o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B_s$-$\bar B_s$ mixing') Prediction('DeltaM_s', lambda wc_obj, par: DeltaM_positive(wc_obj, par, 'Bs')) o = Observable('DeltaM_d') o.set_description(r"Mass difference in the $B^0$-$\bar B^0$ system") o.tex = r"$\Delta M_d$" o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B^0$-$\bar B^0$ mixing') Prediction('DeltaM_d', lambda wc_obj, par: DeltaM_positive(wc_obj, par, 'B0')) o = Observable('DeltaM_d/DeltaM_s') o.set_description(r"Ratio of Mass differences in the $B^0$-$\bar B^0$ and $B_s$-$\bar B_s$ systems") o.tex = r"$\Delta M_d/\Delta M_s$" o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B^0$-$\bar B^0$ mixing') o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B_s$-$\bar B_s$ mixing') Prediction('DeltaM_d/DeltaM_s', lambda wc_obj, par: DeltaM_positive(wc_obj, par, 'B0') / DeltaM_positive(wc_obj, par, 'Bs'))
return num/den def BR_tot_leptonflavour_function(lnum, lden): return lambda wc_obj, par: BR_tot_leptonflavour(wc_obj, par, lnum, lden) _process_taxonomy = r'Process :: $b$ hadron decays :: Semi-leptonic tree-level decays :: $B\to X\ell\nu$ :: $' _lep = {'e': 'e', 'mu': r'\mu', 'tau': r'\tau', 'l': r'\ell'} for l in _lep: _obs_name = "BR(B->Xc"+l+"nu)" _process_tex = r"B\to X_c"+_lep[l]+r"^+\nu_"+_lep[l] _obs = Observable(_obs_name) _obs.set_description(r"Total branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\text{BR}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy + _process_tex + r"$") Prediction(_obs_name, BR_tot_function(l)) # Lepton flavour ratios for l in [('mu','e'), ('tau','mu'), ('tau', 'l')]: _obs_name = "R"+l[0]+l[1]+"(B->Xclnu)" _obs = Observable(name=_obs_name) _process_1 = r"B\to X_c"+_lep[l[0]]+r"^+\nu_"+_lep[l[0]] _process_2 = r"B\to X_c"+_lep[l[1]]+r"^+\nu_"+_lep[l[1]] _obs.set_description(r"Ratio of total branching ratios of $" + _process_1 + r"$" + " and " + r"$" + _process_2 +r"$") _obs.tex = r"$R_{" + _lep[l[0]] + ' ' + _lep[l[1]] + r"}(B\to X_c\ell^+\nu)$" # add taxonomy for both processes (e.g. B->Xcenu and B->Xcmunu) _obs.add_taxonomy(_process_taxonomy + _process_1 + r"$") _obs.add_taxonomy(_process_taxonomy + _process_2 + r"$") Prediction(_obs_name, BR_tot_leptonflavour_function(l[0], l[1]))
def BR_tot_function(B, V, lep): return lambda wc_obj, par: BR_tot(wc_obj, par, B, V, lep) # Observable and Prediction instances _tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau', 'l': r'\ell'} _func = {'dBR/dq2': dBRdq2_function, 'BR': BR_tot_function, '<BR>': BR_binned_function} _desc = {'dBR/dq2': 'Differential', 'BR': 'Total', '<BR>': 'Binned'} _tex_br = {'dBR/dq2': r'\frac{d\text{BR}}{dq^2}', 'BR': r'\text{BR}', '<BR>': r'\langle\text{BR}\rangle'} _args = {'dBR/dq2': ['q2'], 'BR': None, '<BR>': ['q2min', 'q2max']} _hadr = { 'B0->D*': {'tex': r"B^0\to D^{\ast -}", 'B': 'B0', 'V': 'D*+', }, 'B+->D*': {'tex': r"B^+\to D^{\ast 0}", 'B': 'B+', 'V': 'D*0', }, 'B0->rho': {'tex': r"B^0\to \rho^-", 'B': 'B0', 'V': 'rho+', }, 'B+->rho': {'tex': r"B^+\to \rho^0", 'B': 'B+', 'V': 'rho0', }, 'B+->omega': {'tex': r"B^+\to \omega ", 'B': 'B+', 'V': 'omega', }, 'Bs->K*': {'tex': r"B_s\to K^{* -} ", 'B': 'Bs', 'V': 'K*+', }, } for l in ['e', 'mu', 'tau', 'l']: for br in ['dBR/dq2', 'BR', '<BR>']: for M in _hadr.keys(): _process_tex = _hadr[M]['tex']+_tex[l]+r"^+\nu_"+_tex[l] _obs_name = br + "("+M+l+"nu)" _obs = Observable(_obs_name) _obs.set_description(_desc[br] + r" branching ratio of $" + _process_tex + "$") _obs.tex = r'$' + _tex_br[br] + r"(" +_process_tex + ")$" _obs.arguments = _args[br] _obs.add_taxonomy(r'Process :: $b$ hadron decays :: Semi-leptonic tree-level decays :: $B\to V\ell\nu$ :: $' + _process_tex + r'$') Prediction(_obs_name, _func[br](_hadr[M]['B'], _hadr[M]['V'], l))
}, } _process_taxonomy = r'Process :: $b$ hadron decays :: Semi-leptonic tree-level decays :: $B\to V\ell\nu$ :: $' for l in ['e', 'mu', 'tau', 'l']: for br in ['dBR/dq2', 'BR', '<BR>']: for M in _hadr.keys(): _process_tex = _hadr[M]['tex'] + _tex[l] + r"^+\nu_" + _tex[l] _obs_name = br + "(" + M + l + "nu)" _obs = Observable(_obs_name) _obs.set_description(_desc[br] + r" branching ratio of $" + _process_tex + "$") _obs.tex = r'$' + _tex_br[br] + r"(" + _process_tex + ")$" _obs.arguments = _args[br] _obs.add_taxonomy(_process_taxonomy + _process_tex + r'$') Prediction(_obs_name, _func[br](_hadr[M]['B'], _hadr[M]['V'], l)) # Lepton flavour ratios for l in [('mu', 'e'), ('tau', 'mu'), ('tau', 'l')]: for M in _hadr_l.keys(): # binned ratio of BRs _obs_name = "<R" + l[0] + l[1] + ">(" + M + "lnu)" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description(r"Ratio of partial branching ratios of $" + _hadr_l[M]['tex'] + _tex[l[0]] + r"^+ \nu_" + _tex[l[0]] + r"$" + " and " + r"$" + _hadr_l[M]['tex'] + _tex[l[1]] + r"^+ \nu_" + _tex[l[1]] + r"$") _obs.tex = r"$\langle R_{" + _tex[l[0]] + ' ' + _tex[
} for l in ['e', 'mu', 'tau']: for M in _hadr.keys(): _process_tex = _hadr[M]['tex'] + _tex[l] + r"^+" + _tex[l] + r"^-" _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to P\ell^+\ell^-$ :: $' + _process_tex + r"$" for obs in sorted(_observables.keys()): _obs_name = "<" + obs + ">(" + M + l + l + ")" _obs = Observable(name=_obs_name, arguments=['q2min', 'q2max']) _obs.set_description('Binned ' + _observables[obs]['desc'] + r" in $" + _process_tex + r"$") _obs.tex = r"$\langle " + _observables[obs][ 'tex'] + r"\rangle(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction( _obs_name, bpll_obs_int_ratio_func(_observables[obs]['func_num'], dGdq2_cpaverage, _hadr[M]['B'], _hadr[M]['P'], l)) _obs_name = obs + "(" + M + l + l + ")" _obs = Observable(name=_obs_name, arguments=['q2']) _obs.set_description(_observables[obs]['desc'][0].capitalize() + _observables[obs]['desc'][1:] + r" in $" + _process_tex + r"$") _obs.tex = r"$" + _observables[obs][ 'tex'] + r"(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction(
'dBR/dq2': r'\frac{d\text{BR}}{dq^2}', 'BR': r'\text{BR}', '<BR>': r'\langle\text{BR}\rangle' } _args = {'dBR/dq2': ['q2'], 'BR': None, '<BR>': ['q2min', 'q2max']} _hadr = { 'KL->pi': { 'tex': r"K_L\to \pi^+", 'K': 'KL', 'P': 'pi+', }, 'K+->pi': { 'tex': r"K^+\to \pi^0", 'K': 'K+', 'P': 'pi0', }, } for l in ['e', 'mu', 'l']: for M in _hadr.keys(): _process_tex = _hadr[M]['tex'] + _tex[l] + r"^+\nu_" + _tex[l] _process_taxonomy = r'Process :: $s$ hadron decays :: Semi-leptonic tree-level decays :: $K\to P\ell\nu$ :: $' + _process_tex + r"$" _obs_name = "BR(" + M + l + "nu)" _obs = Observable(_obs_name) _obs.set_description(r"Total branching ratio of $" + _process_tex + r"$") _obs.tex = r"$\text{BR}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy) Prediction(_obs_name, BR_tot_function(_hadr[M]['K'], _hadr[M]['P'], l))
wc = wctot_dict(wc_obj, label, scale, par) return ADeltaGamma(par, wc, B, lep) return ADG_func # Observable and Prediction instances _tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau'} for l in ['e', 'mu', 'tau']: _process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to\ell^+\ell^-$ :: $' # For the B^0 decay, we take the time-integrated branching ratio _obs_name = "BR(Bs->"+l+l+")" _obs = Observable(_obs_name) _process_tex = r"B_s\to "+_tex[l]+r"^+"+_tex[l]+r"^-" _obs.set_description(r"Time-integrated branching ratio of $" + _process_tex + r"$.") _obs.tex = r"$\overline{\text{BR}}(" + _process_tex + r")$" _obs.add_taxonomy(_process_taxonomy + _process_tex + r"$") Prediction(_obs_name, bqll_obs_function(br_timeint, 'Bs', l, l)) # Add the effective lifetimes for Bs _obs_name = 'tau_'+l+l _obs = Observable(_obs_name) _obs.set_description(r"Effective lifetime for $"+ _process_tex + r"$.") _obs.tex = r"$\tau_{B_s \to " +_tex[l] +_tex[l] + "}$" _obs.add_taxonomy(_process_taxonomy + _process_tex + r"$") if l=='e': Prediction(_obs_name, lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'e')) if l=='mu': Prediction(_obs_name, lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'mu')) if l=='tau': Prediction(_obs_name, lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'tau'))